1. The problem statement, all variables and given/known data A mass M is split into two parts, m and M - m, which are then separated by a certain distance. What ratio m/M maximizes the magnitude of the gravitational force between the parts? 2. Relevant equations F=Gm1m2/d^2 3. The attempt at a solution I first just tried plugging in M - m and m in for m1 and m2 to see what I get. F=(GMm-Gm)/d^2 I believe that I will have to take a derivative to find the maximum, but I am confused as to what I should take the derivative with respect to.